Simplify the following expression: $\dfrac{10q^3}{60q^2}$ You can assume $q \neq 0$.
Answer: $ \dfrac{10q^3}{60q^2} = \dfrac{10}{60} \cdot \dfrac{q^3}{q^2} $ To simplify $\frac{10}{60}$ , find the greatest common factor (GCD) of $10$ and $60$ $10 = 2 \cdot 5$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(10, 60) = 2 \cdot 5 = 10 $ $ \dfrac{10}{60} \cdot \dfrac{q^3}{q^2} = \dfrac{10 \cdot 1}{10 \cdot 6} \cdot \dfrac{q^3}{q^2} $ $\phantom{ \dfrac{10}{60} \cdot \dfrac{3}{2}} = \dfrac{1}{6} \cdot \dfrac{q^3}{q^2} $ $ \dfrac{q^3}{q^2} = \dfrac{q \cdot q \cdot q}{q \cdot q} = q $ $ \dfrac{1}{6} \cdot q = \dfrac{q}{6} $